Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lumber.

Correct result:

a =  24.749 cm
V =  0.368 m3

Solution:

a=35/2=24.749 cma=35/\sqrt{ 2 }=24.749 \ \text{cm}
V=a2h=0.24726=0.368 m3V = a^2 h = 0.247^2\cdot 6 = 0.368 \ \text{m}^3



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